Finally, we calculate an expression for the fiber swimming speed in terms of the prescribed preferred curvature. The expression depends in a complicated way on the viscoelastic parameters corresponding to the fluid relaxation time and the additional (polymer) viscosity of the fluid. Nevertheless, we are able to make a few predictions about the swimming speed, which we test via numerical simulations. The numerical method that we use is a natural extension of the method we proposed in [1]}, which is based on a combination of the methods used in [2]}, [3]}. We show that varying two viscoelastic parameters corresponding to the fluid relaxation time and the additional polymeric stress of the fluid can have complex effects on the fiber swimming speed. Most strikingly, we find a scenario in which viscoelastic effects cause the swimmer to reverse direction. Our results are for a small set of parameter values and two choices of time-periodic preferred curvature, meaning that much remains to be explored.
